Rewrite as a simplified fraction. ${0.4\overline{2} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 42.2222...\\ 10x &= 4.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 38}$ ${x = \dfrac{38}{90}} $ ${x = \dfrac{19}{45}} $